On the complexity of bounded time and precision reachability for piecewise affine systems

Abstract

Abstract. Reachability for piecewise affine systems is known to be undecidable, starting from dimension 2. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine systems. We show in particular that the region-to-region bounded time versions leads to NP-complete or co-NP-complete problems, starting from dimension 2. We also prove that a bounded precision version leads to P SP ACE-complete problems.

Reachability problems in low-dimensional nondeterministic polynomial maps over integers

“…When considering maps over rationals, the questions can become harder having connections to group theory [14] and number theory [8]. Changing the question from point reachability to staying within a set [15] or set reachability [1], can be made more amenable to analysis.…”